Answer :
Answer:
[tex]f'(x)=-a^2e^{-ax}[/tex]
General Formulas and Concepts:
Calculus
- Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
- Derivative: [tex]\frac{d}{dx} [e^u]=e^u \cdot u'[/tex]
Step-by-step explanation:
Step 1: Define
[tex]f(x)=ae^{-ax}[/tex]
Step 2: Find Derivative
- Derivative eˣ [Chain Rule]: [tex]f'(x)=ae^{-ax} \cdot -a[/tex]
- Condense/Simplify: [tex]f'(x)=-a^2e^{-ax}[/tex]